Numerical analysis of long-range spatial correlations in surface growth.

Area of Science:

• Surface growth dynamics
• Statistical physics
• Nonlinear dynamics

Background:

• Understanding long-range spatial correlations is crucial for modeling complex surface growth phenomena.
• The Kardar-Parisi-Zhang (KPZ) equation is a fundamental model for surface growth, but extensions are needed for correlated noise and nonlocal interactions.
• Investigating the interplay between fractional calculus and spatially correlated noise offers new insights into pattern formation.

Purpose of the Study:

• To numerically analyze long-range spatial correlations in surface growth.
• To study a generalized Kardar-Parisi-Zhang (KPZ) equation incorporating a fractional Laplacian and long-range spatially correlated noise.
• To investigate the interplay between the fractional Laplacian and correlated noise in surface growth systems.

Main Methods:

• Numerical simulations of a generalized Kardar-Parisi-Zhang (KPZ) equation.
• Incorporation of a fractional Laplacian operator to model nonlocal effects.
• Driving the system with long-range spatially correlated noise to study its influence.

Main Results:

• The surface growth system exhibits nontrivial scaling properties.
• These scaling properties show a strong dependence on the noise correlation.
• The fractional order has a weak dependence on the observed scaling properties.
• Growth instability is analyzed across various parameter regimes.

Conclusions:

• Long-range spatial correlations significantly influence surface growth dynamics.
• The interplay between fractional Laplacian and correlated noise leads to complex scaling behaviors.
• The findings provide a deeper understanding of pattern formation in systems with nonlocal interactions and correlated noise.